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Turkey NMO 2008 1st Round - P25 (Geometry)

Source:

August 26, 2012
geometry

Problem Statement

Let CC and DD be points on the circle with center OO and diameter [AB][AB] where CC and DD are on different semicircles with diameter [AB][AB]. Let HH be the foot perpendicular from BB to [CD][CD]. If ∣AO∣=13|AO|=13, ∣AC∣=24|AC|=24, and ∣HD∣=12|HD|=12, what is DCB^\widehat{DCB} in degrees?
<spanclass=′latex−bold′>(A)</span> 30<spanclass=′latex−bold′>(B)</span> 45<spanclass=′latex−bold′>(C)</span> 60<spanclass=′latex−bold′>(D)</span> 75<spanclass=′latex−bold′>(E)</span> 80 <span class='latex-bold'>(A)</span>\ 30 \qquad<span class='latex-bold'>(B)</span>\ 45 \qquad<span class='latex-bold'>(C)</span>\ 60 \qquad<span class='latex-bold'>(D)</span>\ 75 \qquad<span class='latex-bold'>(E)</span>\ 80
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